I'm interesting in numerically simulating (with my own code, not an off-the-shelf package) the motion of a single electrically charged particle in a magnetic field. The field will vary in time and space but probably not fast compared to the cyclotron frequency or the Larmor radius.
There are many well known methods for integrating equations of motion for particles in fields. But the force due to the magnetic field has some special properties such as not changing the kinetic energy of the particle. Are there some numerical procedures that are better adapted to this special case eg. that will give a more accurate simulation and better conserve adiabatic invariants (when they should be conserved)?